Dynamical mean-field theory of the Anderson-Hubbard model with local and non-local disorder in tensor formulation

TL;DR

This paper develops a tensor-based dynamical mean-field theory approach to study the Anderson-Hubbard model with local and non-local disorder, revealing phase transitions in correlated electron systems.

Contribution

It introduces a tensor formulation of DMFT incorporating off-diagonal disorder and applies a novel solver to analyze spectral functions and phase transitions.

Findings

Exact bounds for spectral functions on Bethe lattice

Identification of phase transitions from band insulator to Mott insulator

Demonstration of the method's capability to handle complex disorder scenarios

Abstract

To explore correlated electrons in the presence of local and non-local disorder, the Blackman-Esterling-Berk method for averaging over off-diagonal disorder is implemented into dynamical mean-field theory using tensor notation. The impurity model combining disorder and correlations is solved using the recently developed fork tensor-product state solver, which allows one to calculate the single particle spectral functions on the real-frequency axis. In the absence of off-diagonal hopping, we establish exact bounds of the spectral function of the non-interacting Bethe lattice with coordination number $Z$. In the presence of interaction, the Mott insulating paramagnetic phase of the one-band Hubbard model is computed at zero temperature in alloys with site- and off-diagonal disorder. When the Hubbard $U$ parameter is increased, transitions from an alloy band-insulator through a correlated metal into a Mott insulating phase are found to take place.